calculate the standard deviation of 4800 played hands in a game.

I'm trying to calculate the standard deviation of 4800 played hands in a game. Winning results in +1 and losing results in -1. It's 50,591% for a win and 49,409% chance for a loss.This gives the mean/expected value: 4800*0,50591-4800*0,49409 = 56,928. Now using this standarddeviation to calculate the standard deviation using this formula:
Standard deviation = SQRT(np(1-p)). Insertion of the values gives me:
SQRT(4800*0,50591(1-0,50591)) = 34,63.


So 34,63 is the standarddeviation(if the formula and my processes so far are correct). Now I'm trying to use the density function, from wikipedia https://en.wikipedia.org/wiki/Normal_distribution
which gives me: 1/(34,63*SQRT(2Pi))*e^-((x-56.928^2)/(2*34.63^2))


However, when I try to look on this function my graph does not seem right. Where am I going wrong? Thanks for helping!

WolframAlpha plot

Probability Density Function from the quoted wiki page



Values given:
μ = 4800*0.50591 - 4800*0.49409 = 56.736
σ = Sqrt(np (1-p )) = Sqrt( 4800 * 0.50591 * (1 - 0.50591) ) = 34.6386

Plot of normal distribution using those values